Turbulent energy production peak and its location from inner most log law or power law velocity in a turbulent channel/pipe and Couette flows

The present work deals with the inner most, log law velocity and inner most power law velocity, and the associated Reynolds shear stresses, for turbulent energy production in the buffer layer of a fully developed turbulent channel or pipe and Couette flow. The Reynolds momentum equations have been are analyzed with out any closure model of eddy viscosity, mixing length etc. The equivalence of power law solutions with log law solution is demonstrated for large Reynolds numbers. Turbulent energy production asymptotic theory is presented. In a fully developed turbulent channel/pipe flow the theory shows that the peak of production and its location are universal numbers for large friction Reynolds numbers, but for lower Reynolds number theory show dependence on inverse of friction Reynolds number Rτ−1. For turbulent Couette flow peak of production and its location are universal numbers for all friction Reynolds numbers. The turbulent energy production theory predictions in the buffer layer are compared with experimental and DNS data which support the predictions, that in channel or pipe the prediction depend on friction Reynolds number dependence like Rτ−1 and for Couette flow the predictions are universal numbers.